Republican presidential nominee Donald Trump apologised for past remarks that "may have caused personal pain" as he sought to refocus his message in the face of falling opinion poll numbers in his first speech since shaking up his campaign team this week.

Trump did not cite any examples of such remarks.

The New York businessman has made his "tough talk" and brash style a selling point of his campaign for the November 8th election, rarely apologising in the face of criticism even from within his own party for comments insulting women, Muslims and Mexican immigrants.

In his presidential announcement speech last year, he described some Mexican immigrants as "criminals and rapists."